Finite Group Databasebeta

← C29×#19309 #20314209

Subgroups — C29×#19309 #20314209

Order 7424.

600 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3182C211yesmaximal, characteristic
2C29×#3112C211yesmaximal, characteristic
3C29×#3078C211yesmaximal, characteristic, complemented
4Q8×M16×C29C211yesmaximal, characteristic, complemented
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1696C211yesmaximal, characteristic, complemented
8C29×#1686C211yesmaximal, characteristic, complemented
9C29×#1684C211yesmaximal, characteristic, complemented
10C29×#1678C211yesmaximal, characteristic, complemented
11C29×#1676C211yesmaximal, characteristic, complemented
12C29×#1666C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1560C211yesmaximal, characteristic
15C29×#1559C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C2×C4×Q8×C29C2211yescharacteristic
19C29×#500C2211yescharacteristic
20C29×#492C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#480—21no—
24C29×#479—21no—
25C29×#479—21no—
26C29×#477C2211yescharacteristic
27C29×#477C2211yescharacteristic
28C29×#477C2211yescharacteristic
29C29×#477C2211yescharacteristic
30C29×#475C2211yescharacteristic
31C29×#475C2211yescharacteristic
32C29×#468—21no—
33C29×#468—21no—
34C29×#460C2211yescharacteristic
35C29×#460C2211yescharacteristic
36C29×#448—21no—
37C29×#446—21no—
38C29×#446—21no—
39C29×#446C2211yescharacteristic
40C29×#446C2211yescharacteristic
41C8×Q8×C29C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C29×#440—21no—
44C29×#440—21no—
45C29×#440—21no—
46C29×#440—21no—
47C29×#432C2211yescharacteristic
48C29×#428—21no—
49C29×#423—21no—
50C29×#423C2211yescharacteristic
51C29×#423C2211yescharacteristic
52C29×#419—21no—
53C4×M16×C29—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#333C2211yescharacteristic
62C29×#333C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C22×Q8×C29D411yescharacteristic
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×M16×C29—21no—
74C2×M16×C29—21no—
75C2×M16×C29D411yescharacteristic
76C2×M16×C29D411yescharacteristic
77C29×C4⋊Q8C2311yescharacteristic
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×#127C2311yescharacteristic
81C29×#125—21no—
82C29×#124—21no—
83C29×C22⋊Q8—21no—
84C29×C22⋊Q8—21no—
85C29×#121—21no—
86C29×#121—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29—21no—
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29D411yescharacteristic
92C4×Q8×C29D411yescharacteristic
93C4×Q8×C29C2311yescharacteristic
94C4×Q8×C29C2311yescharacteristic
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C29×#117—21no—
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29D411yescharacteristic
100C2×C42×C29—21no—
101C2×C42×C29C2311yescharacteristic
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×C22⋊C8—21no—
135C29×#97—21no—
136C29×#97—21no—
137C29×#97—21no—
138C29×#97D411yescharacteristic
139C29×#97D411yescharacteristic
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—82no—
145C2×Q8×C29—21no—
146C2×Q8×C29—22no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—41no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×Q8×C29C2×D411yescharacteristic
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—41no—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—41no—
160C22×C4×C29C2×D411yescharacteristic
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29#4111yescharacteristic
163SD16×C29—42no—
164SD16×C29—42no—
165SD16×C29—42no—
166SD16×C29—42no—
167M16×C29—22no—
168M16×C29—41no—
169M16×C29—42no—
170M16×C29—42no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29C2×D411yescharacteristic
178C2×C8×C29C2×D411yescharacteristic
179C2×C8×C29C2×D411yescharacteristic
180C2×C8×C29C2×D411yescharacteristic
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C22⋊C4×C29—41no—
197C22⋊C4×C29—41no—
198C22⋊C4×C29—41no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—41no—
204C42×C29C2×D411yescharacteristic
205C42×C29C2×D411yescharacteristic
206C42×C29#4111yescharacteristic
207C42×C29C2411yescharacteristic
208#19309C2911yesmaximal, characteristic, direct product factor, Sylow
209C23×C29—41no—
210C23×C29#12111yescharacteristic
211Q8×C29—21no—
212Q8×C29—21no—
213Q8×C29—21no—
214Q8×C29—42no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—81no—
218Q8×C29—81no—
219Q8×C29#13712yes—
220D4×C29—41no—
221D4×C29—41no—
222D4×C29—41no—
223D4×C29—41no—
224D4×C29—81no—
225D4×C29—82no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—41no—
235C2×C4×C29—42no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—82no—
240C2×C4×C29—81no—
241C2×C4×C29#12111yescharacteristic
242C2×C4×C29#12111yescharacteristic
243C2×C4×C29#12111yescharacteristic
244C2×C4×C29C22×D411yescharacteristic
245C2×C4×C29C22×D411yescharacteristic
246C2×C4×C29C2×#4111yescharacteristic
247C8×C29—21no—
248C8×C29—21no—
249C8×C29—21no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29—41no—
256C8×C29#13712yes—
257#3182C2×C2911yescharacteristic
258#3112C2×C2911yescharacteristic
259#3078C2×C2911yescharacteristic, complemented
260Q8×M16C2×C2911yescharacteristic, complemented
261#1704C2×C2911yescharacteristic, complemented
262#1698C2×C2911yescharacteristic, complemented
263#1696C2×C2911yescharacteristic, complemented
264#1686C2×C2911yescharacteristic, complemented
265#1684C2×C2911yescharacteristic, complemented
266#1678C2×C2911yescharacteristic, complemented
267#1676C2×C2911yescharacteristic, complemented
268#1666C2×C2911yescharacteristic, complemented
269#1569C2×C2911yescharacteristic, complemented
270#1560C2×C2911yescharacteristic
271#1559C2×C2911yescharacteristic, complemented
272C22×C29—21no—
273C22×C29—21no—
274C22×C29—21no—
275C22×C29—81no—
276C22×C29—81no—
277C22×C29—81no—
278C22×C29C2×#12111yescharacteristic
279C4×C29—21no—
280C4×C29—21no—
281C4×C29—22no—
282C4×C29—21no—
283C4×C29—21no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—81no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29C2×#13711yescharacteristic
291C4×C29C2×#13711yescharacteristic
292C4×C29#57511yescharacteristic
293C4×C29#57511yescharacteristic
294#533C22×C2911yescharacteristic
295#532C22×C2911yescharacteristic
296C2×C4×Q8C22×C2911yescharacteristic
297#500C22×C2911yescharacteristic
298#492C22×C2911yescharacteristic
299#487C22×C2911yescharacteristic
300#486C22×C2911yescharacteristic
301#480—21no—
302#479—21no—
303#479—21no—
304#477C22×C2911yescharacteristic
305#477C22×C2911yescharacteristic
306#477C22×C2911yescharacteristic
307#477C22×C2911yescharacteristic
308#475C22×C2911yescharacteristic
309#475C22×C2911yescharacteristic
310#468—21no—
311#468—21no—
312#460C22×C2911yescharacteristic
313#460C22×C2911yescharacteristic
314#448—21no—
315#446—21no—
316#446—21no—
317#446C22×C2911yescharacteristic
318#446C22×C2911yescharacteristic
319C8×Q8C22×C2911yescharacteristic
320C8×Q8C22×C2911yescharacteristic
321#440—21no—
322#440—21no—
323#440—21no—
324#440—21no—
325#432C22×C2911yescharacteristic
326#428—21no—
327#423—21no—
328#423C22×C2911yescharacteristic
329#423C22×C2911yescharacteristic
330#419—21no—
331C4×M16—21no—
332C4×M16C22×C2911yescharacteristic
333#335C22×C2911yescharacteristic
334#335C22×C2911yescharacteristic
335#334C22×C2911yescharacteristic
336#334C22×C2911yescharacteristic
337#333C22×C2911yescharacteristic
338#333C22×C2911yescharacteristic
339#333C22×C2911yescharacteristic
340#333C22×C2911yescharacteristic
341#332C22×C2911yescharacteristic
342#332C22×C2911yescharacteristic
343#331C22×C2911yescharacteristic
344#331C22×C2911yescharacteristic
345C2×C29—41no—
346C2×C29—161no—
347C2×C29#303711yescharacteristic
348C2×C29#305611yescharacteristic
349C2×C29#306811yescharacteristic
350C2×#41—21no—
351C22×Q8D4×C2911yescharacteristic
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16D4×C2911yescharacteristic
359C2×M16D4×C2911yescharacteristic
360C4⋊Q8C23×C2911yescharacteristic
361C4⋊Q8C23×C2911yescharacteristic
362C4⋊Q8C23×C2911yescharacteristic
363#127C23×C2911yescharacteristic
364#125—21no—
365#124—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368#121—21no—
369#121—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8D4×C2911yescharacteristic
375C4×Q8D4×C2911yescharacteristic
376C4×Q8C23×C2911yescharacteristic
377C4×Q8C23×C2911yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380#117—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4D4×C2911yescharacteristic
383C2×C42—21no—
384C2×C42C23×C2911yescharacteristic
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#106—21no—
392#106—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403C4⋊C8C23×C2911yescharacteristic
404C4⋊C8C23×C2911yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417C22⋊C8—21no—
418#97—21no—
419#97—21no—
420#97—21no—
421#97D4×C2911yescharacteristic
422#97D4×C2911yescharacteristic
423C4×C8—21no—
424C4×C8—21no—
425C4×C8C23×C2911yescharacteristic
426C4×C8C23×C2911yescharacteristic
427C29#1930911yescharacteristic, direct product factor, Sylow
428#41—82no—
429C2×Q8—21no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—41no—
435C2×Q8C2×D4×C2911yescharacteristic
436C2×Q8C2×D4×C2911yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—41no—
444C22×C4C2×D4×C2911yescharacteristic
445C22×C4C2×D4×C2911yescharacteristic
446C22×C4#41×C2911yescharacteristic
447SD16—42no—
448SD16—42no—
449SD16—42no—
450SD16—42no—
451M16—22no—
452M16—41no—
453M16—42no—
454M16—42no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8C2×D4×C2911yescharacteristic
462C2×C8C2×D4×C2911yescharacteristic
463C2×C8C2×D4×C2911yescharacteristic
464C2×C8C2×D4×C2911yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C2911yescharacteristic
479C4⋊C4C2×D4×C2911yescharacteristic
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—41no—
488C42C2×D4×C2911yescharacteristic
489C42C2×D4×C2911yescharacteristic
490C42#41×C2911yescharacteristic
491C42C24×C2911yescharacteristic
492C23—41no—
493C23C29×#12111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502Q8C29×#13712yes—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—81no—
508D4—82no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—81no—
524C2×C4C29×#12111yescharacteristic
525C2×C4C29×#12111yescharacteristic
526C2×C4C29×#12111yescharacteristic
527C2×C4C22×D4×C2911yescharacteristic
528C2×C4C22×D4×C2911yescharacteristic
529C2×C4C2×#41×C2911yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8C29×#13712yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22C2×C29×#12111yescharacteristic
547C4—21no—
548C4—21no—
549C4—22no—
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×C29×#13711yescharacteristic
559C4C2×C29×#13711yescharacteristic
560C4C29×#57511yescharacteristic
561C4C29×#57511yescharacteristic
562C2—41no—
563C2—161no—
564C2C29×#303711yescharacteristic
565C2C29×#305611yescharacteristic
566C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C29×#3078C2semidirect
4. Q8×M16×C29C2semidirect
5. C29×#1704C2semidirect
6. C29×#1698C2semidirect
7. C29×#1696C2semidirect
8. C29×#1686C2semidirect
9. C29×#1684C2semidirect
10. C29×#1678C2semidirect
11. C29×#1676C2semidirect
12. C29×#1666C2semidirect
13. C29×#1569C2semidirect
15. C29×#1559C2semidirect
208. #19309C29direct (N × H)
259. #3078C2×C29semidirect
260. Q8×M16C2×C29semidirect
261. #1704C2×C29semidirect
262. #1698C2×C29semidirect
263. #1696C2×C29semidirect
264. #1686C2×C29semidirect
265. #1684C2×C29semidirect
266. #1678C2×C29semidirect
267. #1676C2×C29semidirect
268. #1666C2×C29semidirect
269. #1569C2×C29semidirect
271. #1559C2×C29semidirect
427. C29#19309direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C29×#31822
C29×#31122
C29×#30782
Q8×M16×C292
C29×#17042
C29×#16982
C29×#16962
C29×#16862
C29×#16842
C29×#16782
C29×#16762
C29×#16662
C29×#15692
C29×#15602
C29×#15592
#1930929